Question: Solve for $x$ and $y$ using elimination. ${-3x+3y = 21}$ ${-2x+4y = 32}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $3$ ${12x-12y = -84}$ $-6x+12y = 96$ Add the top and bottom equations together. $6x = 12$ $\dfrac{6x}{{6}} = \dfrac{12}{{6}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-3x+3y = 21}\thinspace$ to find $y$ ${-3}{(2)}{ + 3y = 21}$ $-6+3y = 21$ $-6{+6} + 3y = 21{+6}$ $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {-2x+4y = 32}\thinspace$ and get the same answer for $y$ : ${-2}{(2)}{ + 4y = 32}$ ${y = 9}$